What is the extreme f(x)=x^2-10x-2,2<= x<= 7 ?

The extreme f(x)=x^2-10x-2,2<= x<= 7 is Maximum(2,-18),Minimum(5,-27),Maximum(7,-23)

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extreme f(x)=x^2-10x-2,2<= x<= 7

extreme points

f (x) = x^{2} - 10 x - 2, 2 \leq x \leq 7

Maximum (2, - 18), Minimum (5, - 27), Maximum (7, - 23)

Solution steps

Find the critical points:

x = 2, x = 5, x = 7

Domain of

x^{2} - 10 x - 2, 2 \leq x \leq 7 : 2 \leq x \leq 7

Find intervals:

Decreasing

: 2 < x < 5,

Increasing

: 5 < x < 7

Plug the extreme point

x = 2

into

x^{2} - 10 x - 2 \Rightarrow y = - 18

Maximum (2, - 18)

Plug the extreme point

x = 5

into

x^{2} - 10 x - 2 \Rightarrow y = - 27

Minimum (5, - 27)

Plug the extreme point

x = 7

into

x^{2} - 10 x - 2 \Rightarrow y = - 23

Maximum (7, - 23)

Maximum (2, - 18), Minimum (5, - 27), Maximum (7, - 23)

f (x, y) = x^{2} + x y - 5 x - 2 y^{2} + 2 y

\frac{x + 2}{x ^{2} - 7 x - 18}

f (x) = ln (y - x^{2}) + ln (2 x - y)

f (x, y) = 2 x^{3} + y^{2} - 4 x y + x^{2} - 24 x + 6 y + 7

\frac{1}{3} x^{3} - 12 x^{2} + 144 x + 2

What is the extreme f(x)=x^2-10x-2,2<= x<= 7 ?
The extreme f(x)=x^2-10x-2,2<= x<= 7 is Maximum(2,-18),Minimum(5,-27),Maximum(7,-23)